9514 1404 393
Answer:
10
Step-by-step explanation:
The n-th triangular number is given by ...
t(n) = n(n+1)/2
We went to find n when t(n) = 55.
55 = n(n+1)/2
110 = n(n+1)
Adding 1/4 completes the square.
110.25 = (n +0.5)^2
√110.25 = n+0.5 . . . . . we are interested in the positive value of n
n = 10.5 -0.5 = 10
The triangular number that has 55 dots in its shape is the 10-th number.
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<em>Additional comment</em>
Here, we have gone to the trouble to formally complete the square to find the value of n. You may realize that it isn't really necessary to go to that trouble.
A reasonable estimate of the value of n is possible by considering that the product n(n+1) is a little more than n², so the value of n will be a little less than √110 ≈ 10.49. The nearest integer is 10, which is the answer we're looking for.
To find the equivalent of the equations U divided by V where as u(x) = x^5 - x^4 + x^2 and v(x) = -x^2, first you have to factor out the U first and came up with (x^2)(x^3-x^2+1) then divide it by -x^2 which cancel the X^2 and the answer would become -(x^3-X^2+1), i hope you are satisfied with my answer
The conversion of 120 barrels to quarts is 20,160
12(8+t) Use distributive
96+12t
Answer:
The correct answer is
Z⁶Y³/Z⁶Y⁴ = 1/Y
Step-by-step explanation:
<u>Points to remember</u>
1). xᵃ * xᵇ = xᵃ⁺ᵇ
2). xᵃ/xᵇ = xᵃ⁻ᵇ
3). x° = 1
4). x⁻ᵃ = 1/xᵃ
The given expression is Z⁶Y³/Z⁶Y⁴
<u>To find the simplification of expression</u>
Z⁶Y³/Z⁶Y⁴ = Z⁶⁻⁶ * Y³⁻⁴
= Z° * Y⁻¹ = 1 * 1/Y = 1/Y
Therefore the value of given expression Z⁶Y³/Z⁶Y⁴ is 1/Y
